Some Trapezoid-type Inequalities for Newly Defined Proportional Caputo-Hybrid Operator

This study starts with the construction of a novel identity for the proportional Caputo-hybrid operator. Building on this identity, we develop several integral inequalities related to the right-hand side of Hermite-Hadamard-type inequalities in the context of the proportional Caputo-hybrid operator. Additionally, we demonstrate that the proposed results improve and generalize some previously established findings in the domain of integral inequalities. Lastly, in order to clarify and improve comprehension of the recently established inequalities, we provide numerous examples together with their graphical representations.